The marked price of an article is 50% above cost price. When marked price is increased by 20% and selling price is increased by 20%, the profit doubles. If original marked price is 300. then original selling price is

Options

A. 200
B. 250
C. 240
D. 275

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Cost Price (CP)
The marked price (MP) of the article is given as 300, and it is stated that this marked price is 50% above the cost price.

To find the cost price, we can use the formula:
\[ \text{MP} = \text{CP} + 0.5 \times \text{CP} = 1.5 \times \text{CP} \]
Thus, we can express the cost price as:
\[ \text{CP} = \frac{\text{MP}}{1.5} = \frac{300}{1.5} = 200 \]

### Step 2: Calculate the New Marked Price (MP')
The marked price is increased by 20%. To find the new marked price:
\[ \text{MP'} = \text{MP} + 0.2 \times \text{MP} = 1.2 \times \text{MP} = 1.2 \times 300 = 360 \]

### Step 3: Let the Original Selling Price (SP) be X
Let the original selling price be \( X \).

### Step 4: Calculate the New Selling Price (SP')
The selling price is also increased by 20%, so the new selling price will be:
\[ \text{SP'} = 1.2 \times X \]

### Step 5: Set Up the Profit Equation
The profit in the original case is:
\[ \text{Profit} = \text{SP} - \text{CP} = X - 200 \]
The profit in the new case is:
\[ \text{Profit'} = \text{SP'} - \text{CP} = 1.2X - 200 \]
According to the problem, the profit doubles when both the marked price and selling price are increased:
\[ 1.2X - 200 = 2(X - 200) \]

### Step 6: Solve the Equation
Expanding the equation:
\[ 1.2X - 200 = 2X - 400 \]
Rearranging gives:
\[ 1.2X - 2X = -400 + 200 \]
\[ -0.8X = -200 \]
Dividing both sides by -0.8:
\[ X = \frac{200}{0.8} = 250 \]

### Conclusion
The original selling price \( X \) is 250.